In search for the ultimate model parameters of reactive ...
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www.DRAFT.ugent.be In search for the ultimate model parameters of reactive magnetron sputtering K. Strijckmans, W.P. Leroy & D. Depla Research Group DRAFT, Ghent University
Transcript of In search for the ultimate model parameters of reactive ...
www.DRAFT.ugent.be
In search for the ultimate model parameters of reactive magnetron
sputtering
K. Strijckmans, W.P. Leroy & D. DeplaResearch Group DRAFT, Ghent University
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Outline
1. Introduction
� Reactive Magnetron Sputtering
� Modeling the technique
2. RSD2009 model
� Input
� Output
3. Hysteresis experiments
� Experimental setup
� Aluminium & Yttrium
4. Finding the unknows
� Fit procedure
� Scan algorithm
5. Results
� Setting
� Correlations
� Understanding: a simplification
6. Summary
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Introduction
RSD model
Hysteresisexperiments
Finding the unknows
Results
SummaryWidely applied technique BUT flawed by hysteresis effect:
• discharge voltage
• deposition rate
• partial pressure of reactive gas (e.g. O2)
Reactive Magnetron Sputter Deposition (RSD)
Magnetron: enhancing sputtering by magnetic confining electrons around the targetReactive: adding reactive gas(es) to form a compound
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Modeling: the approach which meets your needs
e.g. magnetron discharge
Modeling the technique
Technique: dividable in different processes/aspects
• magnetic field
• magnetron discharge (plasma)
• particle-target interaction
• transport in gas phase
• film growth
Our model RSD2009
• an analytical surface
model, originated out of
the Berg model
• describes (steady-state)
hysteresis
• ‘Engine’
� balance equations
� 2nd order reactions
Berg, Thin Solid Films 476 (2005) 215
Depla, J.Phys. D: Appl. Phys.40 (2007) 1957
download RSD2009 free www.draft.ugent.be
Introduction
RSD model
Hysteresisexperiments
Finding the unknows
Results
Summary
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Input of the RSD2009 model
• RSD model describes three parts:
� vacuum chamber by the gas flow balance� target composition� substrate composition
• RSD model parameters
Introduction
RSD model
Hysteresisexperiments
Finding the unknows
Results
Summary
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Input: Experimental determined
• Sputter yield of the metal Ym (EAr(V))
weighting method
• Sticking coefficient αs of O2 on the
substrate
αs =amount of O in deposited layer
amount of arriving O
Saraiva, J.Appl.Phys.107 (2010) 034902
Leroy, Thin Solid Films 518 (2009) 1527
Introduction
RSD model
Hysteresisexperiments
Finding the unknows
Results
Summary
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Input: MC simulations
SRIM models
particle-target interaction
SIMTRA models
metal transport
Ziegler, Nucl. Instr. and Meth. in Phys.
Res. B 219–220 (2004) 1027
Van Aeken, J. Phys D: Appl. Phys.41
(2008) 205307Skew Gaussian fit of implantation profile, counting in:
• incident energy• target composition
∆
−+
∆
−−
∆=
p
p
p
p
p R
Rxerf
R
Rx
Rxp
21
2exp
2
1)( α
π
Multi-cell approach of substrate
download SIMTRA free www.draft.ugent.be
download SRIM free www.srim.org
Introduction
RSD model
Hysteresisexperiments
Finding the unknows
Results
Summary
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Problem: left with 3 unknown parameters
Reason:
• experimental hard to retrieve (k,αt) or big uncertainty (Yc)
• simulated (SRIM) value questionable (Yc)
� although some experimental attempts (αt)
Goal: examine freedom and material dependency of these parameters
Solution: fitting RSD2009 output to experiments
Assumption: no significant dependency on working conditions
Input: Unknowns
Kuschel, J. Appl. Phys. 107 (2010) 103302
Introduction
RSD model
Hysteresisexperiments
Finding the unknows
Results
Summary
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Ouput of the RSD2009 model
� Substrate� Target � Gas flow
Introduction
RSD model
Hysteresisexperiments
Finding the unknows
Results
Summary
RSD model gives:
� surface composition of target and substrate� reactive flow consumptions
not easily measurable
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Ouput of the RSD2009 model
� Substrate
� Target
� Gas flow
� Pressure
Introduction
RSD model
Hysteresisexperiments
Finding the unknows
Results
Summary
RSD model gives:
� surface composition of target and substrate� reactive flow consumptions
� reactive gas pressure
easily measurable
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Experimental setup
Sputter conditions:
• Target Al or Y (D = 5.08 cm)
• Process gas Ar
• Reactive gas O2
• S = 55 L/s or 112 L/s
• Pbase = ~10-4 Pa
• PAr = 0.45 Pa or 0.37 Pa
• I = 0.4 A, 0.5 A or 0.6 A
Hysteresis experiment = stepwise in/decreasing the O2 flow while collecting:
• discharge voltage V and current I
• total pressure Ptot = PAr + PO2
steady state values !
Introduction
RSD model
Hysteresisexperiments
Finding the unknows
Results
Summary
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Hysteresis measurements: Al and Y
Aluminium Yttrium
• choice working conditions well-defined critical points
• 3 measurements at fixed currents I=0.4 A, 0.5 A and 0.6 A
• critical points with resolution of 0.1 sccm
• pumping speed S as slope of measurement
S S
Introduction
RSD model
Hysteresisexperiments
Finding the unknows
Results
Summary
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Fitting procedure: how check a set of parameters?
1
2
3 4 5 6
Fit :
• criteria = the 6 critical O2 flow values
• goodness of the fit = worst match out of 6
• fits are ‘good’ if critical points fall within acceptance tolerance
Simulation :
• includes
� measured V and I variation Ym and Iion
� changing target oxidation oxygen implantation profile
Iion (by SEEY)
• limited to experimental measured part
• cuts off at turning point = critical point
(= experimental resolution)
Introduction
RSD model
Hysteresisexperiments
Finding the unknows
Results
Summary
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Scan algorithm: how it works?
Goal: finding all (xi,yi) combinations that pass the fit criteria
Ingredients :
• starting point (Start) found by slightly modified version
• step size (∆x, ∆y)
• parameter boundaries
• fit procedure + acceptance tolerance
• three lists: rejected, accepted and unfinished
Limitation : only for a connected region
Serialimplementation
illustrated for a 2-D
parameter space
(X,Y)
Introduction
RSD model
Hysteresisexperiments
Finding the unknows
Results
Summary
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Results: setting
5 fit parameters :
Scan algorithm :
• 5-D parameter space (Ym, αs, Yc, αt, k)
• parallel implementation one master + many calculation slaves
• acceptance tolerance = 1.5 × experimental resolution (0.1 sccm)
•Parameter Bounds Al Bounds Y Step size
Ym ±10% 5×10-3
αs 0.075 – 0.139 0.187 – 0.273 5×10-3
Yc 0 – 0.1 5×10-4
αt 0 - 1 5×10-3
k 0 - 2×10-22 5×10-25
Introduction
RSD model
Hysteresisexperiments
Finding the unknows
Results
Summary
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Results: correlations
Reaction rate coefficient k – sputter yield oxide Yc
2-D projections (Yc, k) of 5-D
parameter sets (Ym, αs, Yc, αt, k)
acceptance tolerance =
optimal choice of the remaining
parameters (Ym, αs, αt)
• limited (Yc, k) combinations fit
• sputter yield of Y2O3 lower then of Al2O3
• strong relation between Yc and k
Introduction
RSD model
Hysteresisexperiments
Finding the unknows
Results
Summary
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• more freedom in αt
• sticking coefficient αt of Y2O3 higherthen of Al2O3
• no clear relation between k and αt
• lower k higher αt
Reaction rate coefficient k – sticking coefficient αt
Sputter yield oxide Yc - sticking coefficient αt
same structure of acceptance region
because of
k-Yc relation =
higher k higher Yc
What is the nature of this?
Introduction
RSD model
Hysteresisexperiments
Finding the unknows
Results
Summary
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Understanding: a simplification
( ) )(2),(),(),(
),(),(),(
xpIfItxntxkznt
txn
txntxknt
txn
cMOO
MOM
βθ++−=∂
∂
−=∂
∂
RSD2009 – 2nd order reaction
simplification
implantation profile(skewed Gaussian)
Oxygen implantation profile:
• RSD2009 skewed Gaussian
• simplification local uniform
decouple implantation from reaction
Solution:
• RSD2009 numeric
• simplification analytical
( )
S
scsrb
ste
rb
rbs
rbs
rbsrb
Y
Y
Cknf
zYf
zYf
Y
D
IIfF
θθθ
θ
θ
θ
θθ
=
==
−
−
−=
)(
)1(2
)(2ln
)(2
)(),,( 2
0
2
ste
s CIfF =′ ),,( θ
Depla, Springer Series in Material Science 109 (2008) p.193
Introduction
RSD model
Hysteresisexperiments
Finding the unknows
Results
Summary
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Results: comparison RSD2009 and simplification
2
0),,( knIfF s =′ θAluminium Yttrium
23104 −×=k125.0
048.0
1003.6 22
0
=
=
×=
t
cY
n
α 525.0
019.0
1067.3 22
0
=
=
×=
t
cY
n
α
Introduction
RSD model
Hysteresisexperiments
Finding the unknows
Results
Summary
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Results: k – Yc relation?
( )2
2
01ln2
1
c
sY
kn
fD
I=−− θ
00 )(2 znYfn ss >>θ
css YY ≈)(θ
Simplification describes well poissoned mode:
),,( IfF sθ′
Conclusion : k-Yc relation is embedded in RSD2009 model
Introduction
RSD model
Hysteresisexperiments
Finding the unknows
Results
Summary
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1. The steady-state RSD2009 model describes accurately
the pressure-flow hysteresis of Al and Y in oxygen
2. The parameters k and Yc are closely correlated which
finds its origin in the model itself
3. The remaining fit freedom is marked out
4. The target sticking coefficient of oxygen on Y showed
to be higher then on Al
5. The sputter yield of Y2O3 showed to be lower then of
Al2O3
Summary:Introduction
RSD model
Hysteresisexperiments
Finding the unknows
Results
Summary
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eAcknowledgements
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DRAFT – colleagues:
Introduction
RSD model
Hysteresisexperiments
Finding the unknows
Results
Summary
